Which expression is 5y - 9x + 21y equivalent to after being simplified?
20y + 9x, 26y - 9x, -9x - 16y, or 30xy

Step-by-step explanation:

Q3

(a) If 0 < |x − 1| < δ, then |f(x) − 2| < 2

What this means is, how far can x stray from the x=1 line such that f(x) stays within 2 units of the y=2 line (0 < f(x) < 4).

If we move 2 units left of x=1, we get f(x) = 4.

If we move about 3.5 units right of x=1, we get f(x) = 4.

Therefore, δ can't be more than 2.

(b) If 0 < |x| < δ, then |f(x) − 3| < 1

What this means is, how far can x stray from the x=0 line such that f(x) stays within 1 unit of the y=3 line (2 < f(x) < 4).

If we move 1 unit left of x=0, we get f(x) = 4.

If we move 1 unts right of x=0, we get f(x) = 2.

Therefore, δ can't be more than 1.

Since f(x) isn't continuous within this domain, we can't conclude that the limit exists.

Q4

(a) Yes.  If δ = 0.25, then 0.75 < x < 1.25, and f(x) > 200.

(b) No.  f(1) = 300, so even if δ = 0, f(x) will be less than 400.

(c) Yes.  If δ ≈ 0.1, then 0.9 < x < 1, and f(x) > 450.

Answer:

x=-10

Step-by-step explanation:

3=-(4x+7)+3x

move all terms to the left:

3-(-(4x+7)+3x)=0

calculate terms in parentheses: -(-(4x+7)+3x), so:

-(4x+7)+3x

add all the numbers together, and all the variables

3x-(4x+7)

get rid of parentheses

3x-4x-7

add all the numbers together, and all the variables

-1x-7

Back to the equation:

-(-1x-7)

get rid of parentheses

1x+7+3=0

add all the numbers together, and all the variables

x+10=0

move all terms containing x to the left, all other terms to the right

x=-10

Answer:

k = 2

Step-by-step explanation:

The equation of a line in slope- intercept form is

y = mx + c ( m is the slope and c the y- intercept )

y = - 3x + 5 ← is in slope- intercept form

with slope m = - 3

Parallel lines have equal slopes, thus the 2 points have a slope of - 3

calculate the slope using the slope formula and equate to - 3

m = [tex]\frac{y_{2}-y_{1} }{x_{2}-x_{1} }[/tex]

with (x₁, y₁ ) = (4, - 1) and (x₂, y₂ ) = (k, 5)

m = [tex]\frac{5+1}{k-4}[/tex] = [tex]\frac{6}{k-4}[/tex] = - 3 ( multiply both sides by (k - 4) )

- 3(k - 4) = 6 ( divide both sides by - 3 )

k - 4 = - 2 ( add 4 to both sides )

k = 2

Answer:

[tex]\frac{318}{100}[/tex]

Step-by-step explanation:

A rational number can be expressed as

[tex]\frac{a}{b}[/tex] ← where a and b are integers

The 8 in 3.18 is in the hundredths position, thus

3.18 = [tex]\frac{318}{100}[/tex] ← as a rational number

Answer:

you subtract the exponents

Answer:

obtuse angle

Step-by-step explanation:

m(<CEA)=m(<BED)=88 (vertically opposite angles)

So m(<CEB)+m(<AED)=360-(88+88)=182

m(<CEB)=m(<AED)= 182÷2=92

Answer:

-62570000

Step-by-step explanation:

6.257× -10000000

-62570000

Answer:

BC= 9cm

Step-by-step explanation:

a^2 + b^2 = c^2

The slanted side of the triangle is always going to be 'c' because it is the longest side of the triangle.

I got these numbers because 12^2= 144 and 15^2= 225

Answer:

FH = 36 units

Step-by-step explanation:

Points F, G and H are collinear.

Therefore, by joining segments FG and GH we get a segment FH.

FH = FG + GH

By substituting the values of the segments given in the question,

FH = (3x - 1) + (2x + 2)

     = 5x + 1

Since, GH = 16

2x + 2 = 16

2x = 14

x = 7

Therefore, FH = (5x + 1)

                       = 35 + 1

                       = 36 units

Measure of segment FH = 36 units.

Answer:

The sum of two times a number and six.

or

Two times a number plus six.

Step-by-step explanation:

Step 1: Convert 2a into words

2a = two times a number

Step 2: Convert + 6

+ 6 = the sum of 6 or plus 6

Step 3: Combine to make sentence

The sum of two times a number and six.

Two times a number plus six.

Answer:

The answer is

Step-by-step explanation:

The midpoint M of two endpoints of a line segment can be found by using the formula

[tex]M = ( \frac{x1 + x2}{2} , \: \frac{y1 + y2}{2} )[/tex]

where

(x1 , y1) and (x2 , y2) are the points

From the question the points are

(2,-4) and (6,2)

The midpoint is

[tex]M = ( \frac{2 + 6}{ 2} , \: \frac{ - 4 + 2}{2} ) \\ = ( \frac{8}{2} \: , \: - \frac{2}{2} )[/tex]

We have the final answer as

Hope this helps you

Answer:

The mid point must be (4,-1)

Step-by-step explanation:

mid point= [(X1+X2)/2 , (Y1+Y2)/2]

= [ (2+6)/2 , (-4+2)/2]

= [ 8/4 , -2/2]

= (4, -1)

Answer:

No solution.

Step-by-step explanation:

[tex]2(4m + 1) = 4(3 + 2m)\\[/tex]

Expand:

[tex]2\times4m+2\times1=4\times3+4\times2m[/tex]

[tex]8m+2=12+8m[/tex]

Subtract 2 from both sides:

[tex]8m+2-2=12+8m-2[/tex]

[tex]8m=8m+10[/tex]

Subtract 8m from both sides:

[tex]8m-8m=8m+10-8m[/tex]

[tex]0=10[/tex]

Since both sides are not equal, there is no solution, because the value of m will not affect this end result of [tex]0=10[/tex] which is false.

Answer:

any or all real number, meaning anything works, the equations are equal!

Step-by-step explanation:

2(4m + 1) = 4(3 + 2m)

8m+2=12+8m

8m=10+8m

0=10

this means that m can be any real number

hope this helped!

Answer:

a = 1, b = 4

Step-by-step explanation:

You have worked out part (a) correctly, that is

0.7575... = [tex]\frac{75}{99}[/tex] = [tex]\frac{25}{33}[/tex]

(b)

[tex]\frac{a}{11}[/tex] + [tex]\frac{b}{6}[/tex] = [tex]\frac{25}{33}[/tex]

[tex]\frac{6a+11b}{66}[/tex] = [tex]\frac{25}{33}[/tex]  

Multiply numerator/ denominator of [tex]\frac{25}{33}[/tex] by 2, thus

[tex]\frac{25(2)}{33(2)}[/tex] = [tex]\frac{50}{66}[/tex] , then

[tex]\frac{6a+11b}{66}[/tex] = [tex]\frac{50}{66}[/tex] , thus

6a + 11b = 50

Choose a = 1 ( a positive integer ), then

6(1) + 11b = 50

6 + 11b = 50 ( subtract 6 from both sides )

11b = 44 ( divide both sides by 11 )

b = 4

a = 1, b = 4, so

[tex]\frac{1}{11}[/tex] + [tex]\frac{4}{6}[/tex] = [tex]\frac{25}{33\\}[/tex]

Answer:

$3,270

Step-by-step explanation:

A = P(1 + rt)

First, converting R percent to r a decimal

r = R/100 = 18%/100 = 0.18 per year.

Putting time into years for simplicity,

6 months / 12 months/year = 0.5 years.

Solving our equation:

A = 3000(1 + (0.18 × 0.5)) = 3270

A = $3,270.00

The total amount accrued, principal plus interest, from simple interest on a principal of $3,000.00 at a rate of 18% per year for 0.5 years (6 months) is $3,270.00.

Answer:

Step-by-step explanation:

If  1 out of 7 students are liberal arts majors based on Ms. samuel survey, the  estimate of the number of students who are liberal arts majors if the total number of student in the college s 12,000 can be gotten using the equality expression.

7 students = 1 liberal art major student

12,000 = x liberal art major students

cross multiply

7*x = 12000*1

7x = 12000

divide both sides by 7

7x/7 = 12000/7

x = 1714.29

x≈ 1714

Hence the best estimate for the number of students who are liberal arts majors is 1714 students.

Answer:

-3 2/3

Step-by-step explanation:

If the number is positive and they are asking for the absolute value it's always going to be negative of the number they are asking you for the absolute value of. Same thing if it was a negative 3 2/3 then the absolute value of -3 2/3 would be positive 3 2/3.

I hope this helped! <3

Answer: 3.66..

Step-by-step explanation: absolute value is the value of the number from the number 0 on the number line so, 3 ⅔ in decimals is 3.66... so the answer is 3.66... because that is how much the number is if you are counting from 0.

Answer:

k=3/12

k=.25

Step-by-step explanation:

we need to get k by itself

because 12 is over k we need to get rid of it by moving it to the other side (multiplying) because it is 12/k we need to multiply it by 1/12

This eliminates 12 and leaves us with k=3/12

Answer:

the approximate value of the square root of 8 is 2.828

Answer:

305,200

Step-by-step explanation:

Answer:

12.57

Step-by-step explanation:

Not rounded it would be 12.56637

If you are just replacing pi with 3.14. than your answer would be exactly 12.56.

Answer:

D. 8/4

Step-by-step explanation:

Actually, 8/4 is basically 8 divided by 4, which is 2. And 2 is a whole number not decimal number, so that would be your answer.

The fraction number (8/4) that is equal to the whole number is 2. Then the correct option is D.

A fraction number is a number that represents the part of the whole, where the whole can be any number. It is in the form of numerator and denominator.

A. The fraction number is given as

[tex]\dfrac{3}{6}[/tex]

And it can be written as

[tex]\dfrac{1}{2}[/tex]

B. The fraction number is given as

[tex]\dfrac{7}{8}[/tex]

C. The fraction number is given as

[tex]\dfrac{10}{4}[/tex]

And it can be written as

[tex]\dfrac{5}{2}[/tex]

D. The fraction number is given as

[tex]\dfrac{8}{4}[/tex]

And it can be written as 2.

More about the fraction number link is given below.

https://brainly.com/question/78672

Answer:

(7,-1)

Step-by-step explanation:

Answer:

(7,-1)

Step-by-step explanation:

Midpoint = [(x1+x2)÷2] , [(y1+y2)÷2]

= [(9+5)÷2] , [(-3+1)÷2]

= (7 ,-1)

Answer:

yayz fwee pwoints thwank ywuo

Step-by-step explanation:

Answer:

Yes, many times over.

Step-by-step explanation:

I'm sure there is a typo in the question.

640,000 mg = 0.64 kg

Answer:

a) 6x³ − 5x² − 39x + 35

b) no

Step-by-step explanation:

(2x − 5) (3x² + 5x − 7)

Distribute:

3x² (2x − 5) + 5x (2x − 5) − 7 (2x − 5)

Distribute again:

6x³ − 15x² + 10x² − 25x − 14x + 35

Combine like terms:

6x³ − 5x² − 39x + 35

5x − 2 is the opposite of 2x − 5, so you would get the negative of the answer from part (a).

Answer:

3m/seconds

Step-by-step explanation:

In this problem we are required to solve for linear speed of the rotating wheel

The linear speed =angular speed x raduis

Given data

Radius r= 50cm

Converting from cm to m

50/100= 0.5m

Angular velocity w= 6rad/s

V=wr

V= 6*0.5m

V=3m/s

The linear speed is 3m/seconds

Answer:

get from (4,1) to (2,9) go up 8 and over 2 left (-2) - (4 - 2, 1 + 8), do this again (2 - 2, 9+8) and end up at (0,17) which is the y how do you change 7x+3y=3 into slope intercept form.

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Answer:

y = -4x +10

Slope = -4

Step-by-step explanation:

[tex]8x + 2y = 20[/tex]

Slope intercept form =

[tex]y = mx + b[/tex]

[tex]2y = - 8x + 20[/tex]

Divide both sides of the equation by 2

[tex] \frac{2y}{2} = \frac{ - 8x}{2} + \frac{20}{2} [/tex]

Simplify

[tex]y = - 4x + 10[/tex]

In y= mx+b , m is the slope and the coefficient of x

[tex]m = - 4[/tex]

Answer: x=6.9

Step-by-step explanation:

In the problem, it is stated that y=65.37. All we have to do is plug that into y and solve for x.

65.37= 8.3x + 8.1                [subtract both sides by 8.1]

57.27=8.3x                          [divide both sides by 8.3]

x=6.9

Now, we know x=6.9.

Answer:

6.9

Step-by-step explanation: